Bob Costas is aware of his own limitations. If he feels comfortable anchoring with the condition, then he should continue. As a viewer, it didn't both me. You could see the redness, but it wasn't disgusting by any means. It wasn't even a distraction for me. Bob Costas is such an outstanding talent that he could be missing both eyes and he'd still do a great job.
While I don't blame Bob Costas for giving up since he had a case of Pink Eye, I do not believe it hurt his ability to anchor. Children with pink eye are now encouraged to go to school, as are employees who come down with the symptoms. Pink eye has be determined not to be as damaging or contagious as once thought.
The affliction of pink eye is not life threatening, nor does it threaten function. But it is unsightly. Bob Costas gets paid to have his face on TV. If his face is damaged in some way, he cannot do his work effectively. It becomes a distraction and the impact of the commentary will be lost because everyone will be staring at his eye. He cannot perform.
When someone is doing a news broadcast, they need to have a good appearance so that the people will want to watch them. If this eye infection is making his eye look abnormal, then the public will not want to watch him, and it will make the channel look bad.
Not only is it gross to look at, but it is not ethical or in good taste to come into work with an infectious disease that you made spread to your co-workers. He should stay at home and take whatever antibiotics are prescribed to him so that he can get better and come back to work healthy.